Cramer's Rule 3x3

Problem

Solve the 3x3 linear system A*x = b using Cramer's rule:

x[i] = det(A_i) / det(A)

where A_i is A with column i replaced by b. Return x as a list of floats, or None if det(A) == 0.

Hint

Replace one column at a time and take determinant ratios.

case 1

in: [[[1,0,0],[0,1,0],[0,0,1]],[1,2,3]]

expected: [1,2,3]

case 2

in: [[[2,1,-1],[-3,-1,2],[-2,1,2]],[8,-11,-3]]

expected: [2,3,-1]

case 3

in: [[[1,2,3],[0,1,4],[5,6,0]],[5,6,5]]

expected: [13,-10,4]

case 4

in: [[[1,2,3],[4,5,6],[7,8,9]],[1,1,1]]

expected: null

Starter codePython

def cramer_3x3(A, b):
    # Your code here
    pass

4 test cases · run your code against them in the editor